Prerequisites :-
1) The product of slope of two perpendicular lines is-1 .
2) The slope of two parallel lines is same .
Given two lines to us are ,
This line is in slope intercept form which is [tex] y = mx + c [/tex] . Comparing to which we get ,
Again , the second line given to us is ,
- [tex] 3x + 9y = 18 [/tex]
Convert it into slope intercept form , we have ,
[tex]\implies 3( x + 3y ) = 18 [/tex]
Divide both sides by 3 ,
[tex]\implies x + 3y = 6 [/tex]
Solve for y ,
[tex]\implies y = \dfrac{-x}{3} + 2 [/tex]
On comparing to the slope intercept form ,
- [tex] m_2 = \dfrac{-1}{3}[/tex]
And the product both the slopes is ,
[tex]\implies m_1 \times m_2 = \dfrac{-1}{3}\times 3 =\boxed{\red{-1}}[/tex]
Hence the given two lines are perpendicular .
